Structural Properties of Formal Polynomial Algebras in Noncommuting or Nonassociating Indeterminates
Date of Award:
5-2007
Document Type:
Thesis
Degree Name:
Master of Science (MS)
Department:
Mathematics and Statistics
Committee Chair(s)
Dariusz Wilczynski
Committee
Dariusz Wilczynski
Abstract
In order to enlarge the class of equations provided by traditional polynomials over a binary algebra A to a more useful class of equations, we introduce polynomials in noncommuting or nonassociating indeterminates. We discuss algebraic properties of these formal polynomial algebras and their accompanying polynomial function algebras. We present certain basis results for polynomial algebras, which are used to address the question of zero divisors in a polynomial algebra. We give an analog of the remainder theorem and the factor theorem for polynomials. Particular emphasis is placed on showing the difference between polynomials and polynomial functions. We also provide a brief discussion of polynomial composition and formal derivatives.
Checksum
e6fc1838dfb1e08353eb9d63ec856ae1
Recommended Citation
Ballif, Serge C., "Structural Properties of Formal Polynomial Algebras in Noncommuting or Nonassociating Indeterminates" (2007). All Graduate Theses and Dissertations, Spring 1920 to Summer 2023. 7141.
https://digitalcommons.usu.edu/etd/7141
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